## Acta Mathematica

### Tartar’s conjecture and localization of the quasiconvex hull in $\mathbb{R}^{{2 \times 2}}$

#### Abstract

We give a concrete and surprisingly simple characterization of compact sets $K \subset \mathbb{R}^{{2 \times 2}}$ for which families of approximate solutions to the inclusion problem DuK are compact. In particular our condition is algebraic and can be tested algorithmically. We also prove that the quasiconvex hull of compact sets of 2 × 2 matrices can be localized. This is false for compact sets in higher dimensions in general.

#### Article information

Source
Acta Math. Volume 200, Number 2 (2008), 279-305.

Dates
Received: 20 September 2006
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891981

Digital Object Identifier
doi:10.1007/s11511-008-0028-1

Zentralblatt MATH identifier
05322637

Rights
2008 © Institut Mittag-Leffler

#### Citation

Faraco, Daniel; Székelyhidi, László. Tartar’s conjecture and localization of the quasiconvex hull in $\mathbb{R}^{{2 \times 2}}$. Acta Math. 200 (2008), no. 2, 279--305. doi:10.1007/s11511-008-0028-1. https://projecteuclid.org/euclid.acta/1485891981

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